1 (* Copyright (C) 2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 (* let _profiler = <:profiler<_profiler>>;; *)
28 (* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
30 type rule = SuperpositionRight | SuperpositionLeft | Demodulation
31 type uncomparable = int -> int
34 uncomparable * (* trick to break structural equality *)
37 (Cic.term * (* type *)
38 Cic.term * (* left side *)
39 Cic.term * (* right side *)
40 Utils.comparison) * (* ordering *)
41 Cic.metasenv * (* environment for metas *)
45 | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
46 (* subst, (rule,eq1, eq2,predicate) *)
47 and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
49 (* the hashtbl eq_id -> proof, max_eq_id *)
50 module IntOt = struct type t = int let compare = Pervasives.compare end
51 module M = Map.Make(IntOt)
52 type equality_bag = equality M.t * int
54 type goal = goal_proof * Cic.metasenv * Cic.term
57 let mk_equality_bag () = M.empty, 10000 ;;
59 let freshid (m,i) = (m,i+1), i+1 ;;
61 let add_to_bag (id_to_eq,i) id eq = M.add id eq id_to_eq,i ;;
63 let uncomparable = fun _ -> 0
65 let mk_equality bag (weight,p,(ty,l,r,o),m) =
66 let bag, id = freshid bag in
67 let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
68 let bag = add_to_bag bag id eq in
72 let mk_tmp_equality (weight,(ty,l,r,o),m) =
74 uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
78 let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
79 (weight,proof,(ty,l,r,o),m,id)
82 let _,_,_,_,id = open_equality e in id
86 let string_of_rule = function
87 | SuperpositionRight -> "SupR"
88 | SuperpositionLeft -> "SupL"
89 | Demodulation -> "Demod"
92 let string_of_equality ?env eq =
95 let w, _, (ty, left, right, o), m , id = open_equality eq in
96 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
97 id w (CicPp.ppterm ty)
99 (Utils.string_of_comparison o) (CicPp.ppterm right)
100 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
102 | Some (_, context, _) ->
103 let names = Utils.names_of_context context in
104 let w, _, (ty, left, right, o), m , id = open_equality eq in
105 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
106 id w (CicPp.pp ty names)
107 (CicPp.pp left names) (Utils.string_of_comparison o)
108 (CicPp.pp right names)
109 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
113 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
114 Pervasives.compare s1 s2
117 let rec max_weight_in_proof ((id_to_eq,_) as bag) current =
120 | Step (_, (_,id1,(_,id2),_)) ->
121 let eq1 = M.find id1 id_to_eq in
122 let eq2 = M.find id2 id_to_eq in
123 let (w1,p1,(_,_,_,_),_,_) = open_equality eq1 in
124 let (w2,p2,(_,_,_,_),_,_) = open_equality eq2 in
125 let current = max current w1 in
126 let current = max_weight_in_proof bag current p1 in
127 let current = max current w2 in
128 max_weight_in_proof bag current p2
130 let max_weight_in_goal_proof ((id_to_eq,_) as bag) =
132 (fun current (_,_,id,_,_) ->
133 let eq = M.find id id_to_eq in
134 let (w,p,(_,_,_,_),_,_) = open_equality eq in
135 let current = max current w in
136 max_weight_in_proof bag current p)
138 let max_weight bag goal_proof proof =
139 let current = max_weight_in_proof bag 0 proof in
140 max_weight_in_goal_proof bag current goal_proof
142 let proof_of_id (id_to_eq,_) id =
144 let (_,p,(_,l,r,_),_,_) = open_equality (M.find id id_to_eq) in
148 prerr_endline ("Unable to find the proof of " ^ string_of_int id);
152 let is_in (id_to_eq,_) id =
157 let string_of_proof ?(names=[]) bag p gp =
158 let str_of_pos = function
159 | Utils.Left -> "left"
160 | Utils.Right -> "right"
162 let fst3 (x,_,_) = x in
163 let rec aux margin name =
164 let prefix = String.make margin ' ' ^ name ^ ": " in function
166 Printf.sprintf "%sExact (%s)\n"
167 prefix (CicPp.pp t names)
168 | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
169 Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
170 prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
171 (CicPp.pp pred names)^
172 aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id bag eq1)) ^
173 aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id bag eq2))
178 (fun (r,pos,i,s,t) ->
180 "GOAL: %s %s %d %s %s\n" (string_of_rule r)
181 (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
182 aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id bag i)))
186 let rec depend ((id_to_eq,_) as bag) eq id seen =
187 let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
188 if List.mem ideq seen then
195 | Exact _ -> false,seen
196 | Step (_,(_,id1,(_,id2),_)) ->
197 let seen = ideq::seen in
198 let eq1 = M.find id1 id_to_eq in
199 let eq2 = M.find id2 id_to_eq in
200 let b1,seen = depend bag eq1 id seen in
201 if b1 then b1,seen else depend bag eq2 id seen
204 let depend bag eq id = fst (depend bag eq id []);;
206 let ppsubst = Subst.ppsubst ~names:[];;
208 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
209 let build_ens uri termlist =
210 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
212 | Cic.Constant (_, _, _, uris, _) ->
213 (* assert (List.length uris <= List.length termlist); *)
214 let rec aux = function
216 | (uri::uris), (term::tl) ->
217 let ens, args = aux (uris, tl) in
218 (uri, term)::ens, args
219 | _, _ -> assert false
225 let mk_sym uri ty t1 t2 p =
226 let ens, args = build_ens uri [ty;t1;t2;p] in
227 Cic.Appl (Cic.Const(uri, ens) :: args)
230 let mk_trans uri ty t1 t2 t3 p12 p23 =
231 let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
232 Cic.Appl (Cic.Const (uri, ens) :: args)
235 let mk_eq_ind uri ty what pred p1 other p2 =
236 let ens, args = build_ens uri [ty; what; pred; p1; other; p2] in
237 Cic.Appl (Cic.Const (uri, ens) :: args)
240 let p_of_sym ens tl =
241 let args = List.map snd ens @ tl in
247 let open_trans ens tl =
248 let args = List.map snd ens @ tl in
250 | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
254 let open_sym ens tl =
255 let args = List.map snd ens @ tl in
257 | [ty;l;r;p] -> ty,l,r,p
261 let open_eq_ind args =
263 | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
269 | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]))
270 when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
271 | _ -> Utils.debug_print (lazy (CicPp.ppterm pred)); assert false
275 CicSubstitution.subst (Cic.Implicit None) t <>
276 CicSubstitution.subst (Cic.Rel 1) t
279 let canonical t context menv =
280 let remove_cycles t =
283 Cic.Appl (Cic.Const (uri_trans,_)::_)
284 when LibraryObjects.is_trans_eq_URI uri_trans ->
289 Cic.Appl (Cic.Const (uri_trans,ens)::tl)
290 when LibraryObjects.is_trans_eq_URI uri_trans ->
291 let ty,l,m,r,p1,p2 = open_trans ens tl in
292 (if is_transitive p1 then fst (collect p1) else [l,p1]) @
293 (if is_transitive p2 then fst (collect p2) else [m,p2]),
295 | t -> assert false in
296 let rec cut_to_last_duplicate l acc =
299 | (l',p)::tl when l=l' ->
301 Utils.debug_print (lazy ("!!! RISPARMIO " ^ string_of_int (List.length acc) ^ " PASSI"));
302 cut_to_last_duplicate l [l',p] tl
304 cut_to_last_duplicate l ((l',p)::acc) tl
308 (l,_)::_::_ as steps, ((r,uri_trans,ty) as last) ->
309 (match cut_to_last_duplicate l [] steps with
310 (l,p1)::((m,_)::_::_ as tl) ->
311 mk_trans uri_trans ty l m r p1 (rebuild (tl,last))
312 | [l,p1 ; m,p2] -> mk_trans uri_trans ty l m r p1 p2
314 | [] -> assert false)
317 if is_transitive t then
322 let rec remove_refl t =
324 | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
325 when LibraryObjects.is_trans_eq_URI uri_trans ->
326 let ty,l,m,r,p1,p2 = open_trans ens tl in
328 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
330 | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
332 | _ -> Cic.Appl (List.map remove_refl args))
333 | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
334 | Cic.LetIn (name,bo,ty,rest) ->
335 Cic.LetIn (name,remove_refl bo,remove_refl ty,remove_refl rest)
338 let rec canonical_trough_lambda context = function
339 | Cic.Lambda(name,ty,bo) ->
340 let context' = (Some (name,Cic.Decl ty))::context in
341 Cic.Lambda(name,ty,canonical_trough_lambda context' bo)
342 | t -> canonical context t
344 and canonical context t =
346 | Cic.LetIn(name,bo,ty,rest) ->
347 let bo = canonical_trough_lambda context bo in
348 let ty = canonical_trough_lambda context ty in
349 let context' = (Some (name,Cic.Def (bo,ty)))::context in
350 Cic.LetIn(name,bo,ty,canonical context' rest)
351 | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
352 when LibraryObjects.is_sym_eq_URI uri_sym ->
353 (match p_of_sym ens tl with
354 | Cic.Appl ((Cic.Const(uri,ens))::tl)
355 when LibraryObjects.is_sym_eq_URI uri ->
356 canonical context (p_of_sym ens tl)
357 | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
358 when LibraryObjects.is_trans_eq_URI uri_trans ->
359 let ty,l,m,r,p1,p2 = open_trans ens tl in
360 mk_trans uri_trans ty r m l
361 (canonical context (mk_sym uri_sym ty m r p2))
362 (canonical context (mk_sym uri_sym ty l m p1))
363 | Cic.Appl (([Cic.Const(uri_feq,ens);ty1;ty2;f;x;y;p]))
364 when LibraryObjects.is_eq_f_URI uri_feq ->
365 let eq = LibraryObjects.eq_URI_of_eq_f_URI uri_feq in
367 Cic.Const (LibraryObjects.eq_f_sym_URI ~eq, [])
369 let rc = Cic.Appl [eq_f_sym;ty1;ty2;f;x;y;p] in
370 Utils.debug_print (lazy ("CANONICAL " ^ CicPp.ppterm rc));
372 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
373 when LibraryObjects.is_eq_URI uri -> t
374 | _ -> Cic.Appl (List.map (canonical context) args))
375 | Cic.Appl l -> Cic.Appl (List.map (canonical context) l)
378 remove_cycles (remove_refl (canonical context t))
381 let compose_contexts ctx1 ctx2 =
382 ProofEngineReduction.replace_lifting
383 ~equality:(fun _ ->(=)) ~context:[] ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
386 let put_in_ctx ctx t =
387 ProofEngineReduction.replace_lifting
388 ~equality:(fun _ -> (=)) ~context:[] ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
391 let mk_eq uri ty l r =
392 let ens, args = build_ens uri [ty; l; r] in
393 Cic.Appl (Cic.MutInd(uri,0,ens) :: args)
396 let mk_refl uri ty t =
397 let ens, args = build_ens uri [ty; t] in
398 Cic.Appl (Cic.MutConstruct(uri,0,1,ens) :: args)
401 let open_eq = function
402 | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
407 let mk_feq uri_feq ty ty1 left pred right t =
408 let ens, args = build_ens uri_feq [ty;ty1;pred;left;right;t] in
409 Cic.Appl (Cic.Const(uri_feq,ens) :: args)
412 let rec look_ahead aux = function
413 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) as t
414 when LibraryObjects.is_eq_ind_URI uri_ind ||
415 LibraryObjects.is_eq_ind_r_URI uri_ind ->
416 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
417 let ty2,eq,lp,rp = open_pred pred in
418 let hole = Cic.Implicit (Some `Hole) in
419 let ty2 = CicSubstitution.subst hole ty2 in
420 aux ty1 (CicSubstitution.subst other lp) (CicSubstitution.subst other rp) hole ty2 t
421 | Cic.Lambda (n,s,t) -> Cic.Lambda (n,s,look_ahead aux t)
425 let contextualize uri ty left right t =
426 let hole = Cic.Implicit (Some `Hole) in
427 (* aux [uri] [ty] [left] [right] [ctx] [ctx_ty] [t]
429 * the parameters validate this invariant
430 * t: eq(uri) ty left right
431 * that is used only by the base case
433 * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
434 * ctx_ty is the type of ctx
436 let rec aux uri ty left right ctx_d ctx_ty t =
438 | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
439 when LibraryObjects.is_sym_eq_URI uri_sym ->
440 let ty,l,r,p = open_sym ens tl in
441 mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
442 | Cic.LetIn (name,body,bodyty,rest) ->
444 (name,look_ahead (aux uri) body, bodyty,
445 aux uri ty left right ctx_d ctx_ty rest)
446 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
447 when LibraryObjects.is_eq_ind_URI uri_ind ||
448 LibraryObjects.is_eq_ind_r_URI uri_ind ->
449 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
450 let ty2,eq,lp,rp = open_pred pred in
451 let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
452 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
453 let is_not_fixed_lp = is_not_fixed lp in
454 let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
455 (* extract the context and the fixed term from the predicate *)
457 let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
458 (* they were under a lambda *)
459 let m = CicSubstitution.subst hole m in
460 let ctx_c = CicSubstitution.subst hole ctx_c in
461 let ty2 = CicSubstitution.subst hole ty2 in
464 (* create the compound context and put the terms under it *)
465 let ctx_dc = compose_contexts ctx_d ctx_c in
466 let dc_what = put_in_ctx ctx_dc what in
467 let dc_other = put_in_ctx ctx_dc other in
468 (* m is already in ctx_c so it is put in ctx_d only *)
469 let d_m = put_in_ctx ctx_d m in
470 (* we also need what in ctx_c *)
471 let c_what = put_in_ctx ctx_c what in
472 (* now put the proofs in the compound context *)
473 let p1 = (* p1: dc_what = d_m *)
474 if is_not_fixed_lp then
475 aux uri ty2 c_what m ctx_d ctx_ty p1
477 mk_sym uri_sym ctx_ty d_m dc_what
478 (aux uri ty2 m c_what ctx_d ctx_ty p1)
480 let p2 = (* p2: dc_other = dc_what *)
482 mk_sym uri_sym ctx_ty dc_what dc_other
483 (aux uri ty1 what other ctx_dc ctx_ty p2)
485 aux uri ty1 other what ctx_dc ctx_ty p2
487 (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
488 if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
489 let a,b,c,paeqb,pbeqc =
490 if is_not_fixed_lp then
491 dc_other,dc_what,d_m,p2,p1
493 d_m,dc_what,dc_other,
494 (mk_sym uri_sym ctx_ty dc_what d_m p1),
495 (mk_sym uri_sym ctx_ty dc_other dc_what p2)
497 mk_trans uri_trans ctx_ty a b c paeqb pbeqc
498 | t when ctx_d = hole -> t
500 (* let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in *)
501 (* let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in *)
503 let uri_feq = LibraryObjects.eq_f_URI ~eq:uri in
505 (* let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in *)
507 let ctx_d = CicSubstitution.lift 1 ctx_d in
508 put_in_ctx ctx_d (Cic.Rel 1)
510 (* let lty = CicSubstitution.lift 1 ctx_ty in *)
511 (* Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r)) *)
512 Cic.Lambda (Cic.Name "foo",ty,l)
514 (* let d_left = put_in_ctx ctx_d left in *)
515 (* let d_right = put_in_ctx ctx_d right in *)
516 (* let refl_eq = mk_refl uri ctx_ty d_left in *)
517 (* mk_sym uri_sym ctx_ty d_right d_left *)
518 (* (mk_eq_ind uri_ind ty left pred refl_eq right t) *)
519 (mk_feq uri_feq ty ctx_ty left pred right t)
521 aux uri ty left right hole ty t
524 let contextualize_rewrites t ty =
525 let eq,ty,l,r = open_eq ty in
526 contextualize eq ty l r t
529 let add_subst subst =
531 | Exact t -> Exact (Subst.apply_subst subst t)
532 | Step (s,(rule, id1, (pos,id2), pred)) ->
533 Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
536 let build_proof_step eq lift subst p1 p2 pos l r pred =
537 let p1 = Subst.apply_subst_lift lift subst p1 in
538 let p2 = Subst.apply_subst_lift lift subst p2 in
539 let l = CicSubstitution.lift lift l in
540 let l = Subst.apply_subst_lift lift subst l in
541 let r = CicSubstitution.lift lift r in
542 let r = Subst.apply_subst_lift lift subst r in
543 let pred = CicSubstitution.lift lift pred in
544 let pred = Subst.apply_subst_lift lift subst pred in
547 | Cic.Lambda (_,ty,body) -> ty,body
551 if pos = Utils.Left then l,r else r,l
556 mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
558 mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
563 let parametrize_proof p l r =
564 let uniq l = HExtlib.list_uniq (List.sort (fun (i,_) (j,_) -> Pervasives.compare i j) l) in
565 let mot = CicUtil.metas_of_term_set in
566 let parameters = uniq (mot p @ mot l @ mot r) in
567 (* ?if they are under a lambda? *)
570 HExtlib.list_uniq (List.sort Pervasives.compare parameters)
573 (* resorts l such that *hopefully* dependencies can be inferred *)
574 let guess_dependency p l =
576 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
577 when LibraryObjects.is_eq_ind_URI uri_ind ||
578 LibraryObjects.is_eq_ind_r_URI uri_ind ->
579 let ty,_,_,_,_,_ = open_eq_ind tl in
580 let metas = CicUtil.metas_of_term ty in
582 List.partition (fun (i,_) -> List.exists (fun (j,_) -> j=i) metas) l
587 let parameters = guess_dependency p parameters in
588 let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
589 let with_what, lift_no =
590 List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
592 let p = CicSubstitution.lift (lift_no-1) p in
594 ProofEngineReduction.replace_lifting
595 ~equality:(fun _ t1 t2 ->
596 match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
598 ~what ~with_what ~where:p
600 let ty_of_m _ = Cic.Implicit (Some `Type) in
603 (fun (instance,p,n) m ->
606 (Cic.Name ("X"^string_of_int n),
607 CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
613 let instance = match args with | [x] -> x | _ -> Cic.Appl args in
617 let wfo bag goalproof proof id =
619 let p,_,_ = proof_of_id bag id in
621 | Exact _ -> if (List.mem id acc) then acc else id :: acc
622 | Step (_,(_,id1, (_,id2), _)) ->
623 let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
624 let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
630 | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
632 List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
635 let string_of_id (id_to_eq,_) names id =
636 if id = 0 then "" else
638 let (_,p,(t,l,r,_),m,_) = open_equality (M.find id id_to_eq) in
641 Printf.sprintf "%d = %s: %s = %s [%s]" id
642 (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
644 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
645 | Step (_,(step,id1, (dir,id2), p) ) ->
646 Printf.sprintf "%6d: %s %6d %6d %s =(%s) %s [%s]" id
647 (string_of_rule step)
648 id1 id2 (CicPp.pp l names) (CicPp.pp t names) (CicPp.pp r names)
649 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
652 Not_found -> assert false
654 let pp_proof bag names goalproof proof subst id initial_goal =
655 String.concat "\n" (List.map (string_of_id bag names) (wfo bag goalproof proof id)) ^
658 (fst (List.fold_right
659 (fun (r,pos,i,s,pred) (acc,g) ->
660 let _,_,left,right = open_eq g in
663 | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
664 | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
666 let ty = Subst.apply_subst s ty in
667 ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
668 ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
669 "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
672 let rec find_deps bag m i =
675 let p,_,_ = proof_of_id bag i in
677 | Exact _ -> M.add i [] m
678 | Step (_,(_,id1,(_,id2),_)) ->
679 let m = find_deps bag m id1 in
680 let m = find_deps bag m id2 in
681 (* without the uniq there is a stack overflow doing concatenation *)
682 let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in
683 let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
687 let topological_sort bag l =
688 (* build the partial order relation *)
689 let m = List.fold_left (fun m i -> find_deps bag m i) M.empty l in
690 let m = (* keep only deps inside l *)
693 M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m')
696 let m = M.map (fun x -> Some x) m in
698 let keys m = M.fold (fun i _ acc -> i::acc) m [] in
699 let split l m = List.filter (fun i -> M.find i m = Some []) l in
702 (fun k v -> if List.mem k l then None else
705 | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
710 let ok = split keys m in
711 let m = purge ok m in
712 let res = ok @ res in
713 if ok = [] then res else aux m res
715 let rc = List.rev (aux m []) in
719 (* returns the list of ids that should be factorized *)
720 let get_duplicate_step_in_wfo bag l p =
721 let ol = List.rev l in
722 let h = Hashtbl.create 13 in
723 (* NOTE: here the n parameter is an approximation of the dependency
724 between equations. To do things seriously we should maintain a
725 dependency graph. This approximation is not perfect. *)
727 let p,_,_ = proof_of_id bag i in
732 let no = Hashtbl.find h i in
733 Hashtbl.replace h i (no+1);
735 with Not_found -> Hashtbl.add h i 1;true
737 let rec aux = function
739 | Step (_,(_,i1,(_,i2),_)) ->
740 let go_on_1 = add i1 in
741 let go_on_2 = add i2 in
742 if go_on_1 then aux (let p,_,_ = proof_of_id bag i1 in p);
743 if go_on_2 then aux (let p,_,_ = proof_of_id bag i2 in p)
747 (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id bag id in p))
749 (* now h is complete *)
750 let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
751 let proofs = List.filter (fun (_,c) -> c > 1) proofs in
752 let res = topological_sort bag (List.map (fun (i,_) -> i) proofs) in
756 let build_proof_term bag eq h lift proof =
757 let proof_of_id aux id =
758 let p,l,r = proof_of_id bag id in
759 try List.assoc id h,l,r with Not_found -> aux p, l, r
761 let rec aux = function
763 CicSubstitution.lift lift term
764 | Step (subst,(rule, id1, (pos,id2), pred)) ->
765 let p1,_,_ = proof_of_id aux id1 in
766 let p2,l,r = proof_of_id aux id2 in
769 | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
770 | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
775 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
778 let p = build_proof_step eq lift subst p1 p2 pos l r pred in
779 (* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
781 prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
788 let build_goal_proof ?(contextualize=true) ?(forward=false) bag eq l initial ty se context menv =
789 let se = List.map (fun i -> Cic.Meta (i,[])) se in
790 let lets = get_duplicate_step_in_wfo bag l initial in
791 let letsno = List.length lets in
792 let l = if forward then List.rev l else l in
793 let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l in
797 let p,l,r = proof_of_id bag id in
798 let cic = build_proof_term bag eq h n p in
799 let real_cic,instance =
800 parametrize_proof cic l r
802 let h = (id, instance)::lift_list h in
803 acc@[id,real_cic],n+1,h)
807 List.map (fun (id,cic) -> id,cic,Cic.Implicit (Some `Type)) lets
810 let rec aux se current_proof = function
811 | [] -> current_proof,se
812 | (rule,pos,id,subst,pred)::tl ->
813 let p,l,r = proof_of_id bag id in
814 let p = build_proof_term bag eq h letsno p in
815 let pos = if forward then pos else
816 if pos = Utils.Left then Utils.Right else Utils.Left in
819 | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
820 | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
825 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
829 build_proof_step eq letsno subst current_proof p pos l r pred
831 let proof,se = aux se proof tl in
832 Subst.apply_subst_lift letsno subst proof,
833 List.map (fun x -> Subst.apply_subst(*_lift letsno*) subst x) se
835 aux se (build_proof_term bag eq h letsno initial) l
838 let initial = proof in
840 (fun (id,cic,ty) (n,p) ->
843 Cic.Name ("H"^string_of_int id),
847 lets (letsno-1,initial)
851 then contextualize_rewrites proof (CicSubstitution.lift letsno ty)
853 canonical proof context menv, se
856 let refl_proof eq_uri ty term =
857 Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
860 let metas_of_proof bag p =
862 match LibraryObjects.eq_URI () with
866 (ProofEngineTypes.Fail
867 (lazy "No default equality defined when calling metas_of_proof"))
869 let p = build_proof_term bag eq [] 0 p in
870 Utils.metas_of_term p
873 let remove_local_context eq =
874 let w, p, (ty, left, right, o), menv,id = open_equality eq in
875 let p = Utils.remove_local_context p in
876 let ty = Utils.remove_local_context ty in
877 let left = Utils.remove_local_context left in
878 let right = Utils.remove_local_context right in
879 w, p, (ty, left, right, o), menv, id
882 let relocate newmeta menv to_be_relocated =
883 let subst, newmetasenv, newmeta =
885 (fun i (subst, metasenv, maxmeta) ->
886 let _,context,ty = CicUtil.lookup_meta i menv in
888 let newmeta = Cic.Meta(maxmeta,irl) in
889 let newsubst = Subst.buildsubst i context newmeta ty subst in
890 (* newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1) *)
891 newsubst, (maxmeta,[],ty)::metasenv, maxmeta+1)
892 to_be_relocated (Subst.empty_subst, [], newmeta+1)
894 (* let subst = Subst.flatten_subst subst in *)
895 let menv = Subst.apply_subst_metasenv subst (menv @ newmetasenv) in
898 let fix_metas_goal (id_to_eq,newmeta) goal =
899 let (proof, menv, ty) = goal in
900 let to_be_relocated = List.map (fun i ,_,_ -> i) menv in
901 let subst, menv, newmeta = relocate newmeta menv to_be_relocated in
902 let ty = Subst.apply_subst subst ty in
905 | [] -> assert false (* is a nonsense to relocate the initial goal *)
906 | (r,pos,id,s,p) :: tl -> (r,pos,id,Subst.concat subst s,p) :: tl
908 (id_to_eq,newmeta+1),(proof, menv, ty)
911 let fix_metas (id_to_eq, newmeta) eq =
912 let w, p, (ty, left, right, o), menv,_ = open_equality eq in
913 let to_be_relocated = List.map (fun i ,_,_ -> i) menv in
914 let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
915 let ty = Subst.apply_subst subst ty in
916 let left = Subst.apply_subst subst left in
917 let right = Subst.apply_subst subst right in
918 let fix_proof = function
919 | Exact p -> Exact (Subst.apply_subst subst p)
920 | Step (s,(r,id1,(pos,id2),pred)) ->
921 Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
923 let p = fix_proof p in
924 let bag = id_to_eq, newmeta in
925 let bag, e = mk_equality bag (w, p, (ty, left, right, o), metasenv) in
929 exception NotMetaConvertible;;
931 let meta_convertibility_aux table t1 t2 =
932 let module C = Cic in
933 let rec aux ((table_l,table_r) as table) t1 t2 =
935 | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 = m2 -> table
936 | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 < m2 -> aux table t2 t1
937 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
938 let m1_binding, table_l =
939 try List.assoc m1 table_l, table_l
940 with Not_found -> m2, (m1, m2)::table_l
941 and m2_binding, table_r =
942 try List.assoc m2 table_r, table_r
943 with Not_found -> m1, (m2, m1)::table_r
945 if (m1_binding <> m2) || (m2_binding <> m1) then
946 raise NotMetaConvertible
948 | C.Var (u1, ens1), C.Var (u2, ens2)
949 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
950 aux_ens table ens1 ens2
951 | C.Cast (s1, t1), C.Cast (s2, t2)
952 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
953 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2) ->
954 let table = aux table s1 s2 in
956 | C.LetIn (_, s1, ty1, t1), C.LetIn (_, s2, ty2, t2) ->
957 let table = aux table s1 s2 in
958 let table = aux table ty1 ty2 in
960 | C.Appl l1, C.Appl l2 -> (
961 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
962 with Invalid_argument _ -> raise NotMetaConvertible
964 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
965 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
966 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
967 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
968 aux_ens table ens1 ens2
969 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
970 when (UriManager.eq u1 u2) && i1 = i2 ->
971 let table = aux table s1 s2 in
972 let table = aux table t1 t2 in (
973 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
974 with Invalid_argument _ -> raise NotMetaConvertible
976 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
979 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
980 if i1 <> i2 then raise NotMetaConvertible
982 let res = (aux res s1 s2) in aux res t1 t2)
984 with Invalid_argument _ -> raise NotMetaConvertible
986 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
989 (fun res (n1, s1, t1) (n2, s2, t2) ->
990 let res = aux res s1 s2 in aux res t1 t2)
992 with Invalid_argument _ -> raise NotMetaConvertible
994 | t1, t2 when t1 = t2 -> table
995 | _, _ -> raise NotMetaConvertible
997 and aux_ens table ens1 ens2 =
998 let cmp (u1, t1) (u2, t2) =
999 Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
1001 let ens1 = List.sort cmp ens1
1002 and ens2 = List.sort cmp ens2 in
1005 (fun res (u1, t1) (u2, t2) ->
1006 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
1009 with Invalid_argument _ -> raise NotMetaConvertible
1015 let meta_convertibility_eq eq1 eq2 =
1016 let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
1017 let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
1020 else if (left = left') && (right = right') then
1022 else if (left = right') && (right = left') then
1026 let table = meta_convertibility_aux ([],[]) left left' in
1027 let _ = meta_convertibility_aux table right right' in
1029 with NotMetaConvertible ->
1031 let table = meta_convertibility_aux ([],[]) left right' in
1032 let _ = meta_convertibility_aux table right left' in
1034 with NotMetaConvertible ->
1038 let meta_convertibility t1 t2 =
1043 ignore(meta_convertibility_aux ([],[]) t1 t2);
1045 with NotMetaConvertible ->
1049 let meta_convertibility_subst t1 t2 menv =
1054 let (l,_) = meta_convertibility_aux ([],[]) t1 t2 in
1059 let (_,c,t) = CicUtil.lookup_meta x menv in
1061 CicMkImplicit.identity_relocation_list_for_metavariable c in
1062 (y,(c,Cic.Meta(x,irl),t))
1063 with CicUtil.Meta_not_found _ ->
1065 let (_,c,t) = CicUtil.lookup_meta y menv in
1067 CicMkImplicit.identity_relocation_list_for_metavariable c in
1068 (x,(c,Cic.Meta(y,irl),t))
1069 with CicUtil.Meta_not_found _ -> assert false) l in
1071 with NotMetaConvertible ->
1075 exception TermIsNotAnEquality;;
1077 let term_is_equality term =
1079 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
1080 when LibraryObjects.is_eq_URI uri -> true
1084 let equality_of_term bag proof term newmetas =
1086 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2]
1087 when LibraryObjects.is_eq_URI uri ->
1088 let o = !Utils.compare_terms t1 t2 in
1089 let stat = (ty,t1,t2,o) in
1090 let w = Utils.compute_equality_weight stat in
1091 let bag, e = mk_equality bag (w, Exact proof, stat,newmetas) in
1094 raise TermIsNotAnEquality
1097 let is_weak_identity eq =
1098 let _,_,(_,left, right,_),_,_ = open_equality eq in
1100 (* doing metaconv here is meaningless *)
1103 let is_identity (_, context, ugraph) eq =
1104 let _,_,(ty,left,right,_),menv,_ = open_equality eq in
1105 (* doing metaconv here is meaningless *)
1107 (* fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
1112 let term_of_equality eq_uri equality =
1113 let _, _, (ty, left, right, _), menv, _= open_equality equality in
1114 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
1115 let argsno = List.length menv in
1117 CicSubstitution.lift argsno
1118 (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
1122 (fun (i,_,ty) (n, t) ->
1123 let name = Cic.Name ("X" ^ (string_of_int n)) in
1124 let ty = CicSubstitution.lift (n-1) ty in
1126 ProofEngineReduction.replace
1127 ~equality:eq ~what:[i]
1128 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
1130 (n-1, Cic.Prod (name, ty, t)))
1134 let symmetric bag eq_ty l id uri m =
1135 let eq = Cic.MutInd(uri,0,[]) in
1137 Cic.Lambda (Cic.Name "Sym",eq_ty,
1138 Cic.Appl [CicSubstitution.lift 1 eq ;
1139 CicSubstitution.lift 1 eq_ty;
1140 Cic.Rel 1;CicSubstitution.lift 1 l])
1144 [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
1147 let bag, eq = mk_equality bag (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
1148 let (_,_,_,_,id) = open_equality eq in
1151 bag, Step(Subst.empty_subst,
1152 (Demodulation,id1,(Utils.Left,id),pred))
1155 module IntOT = struct
1157 let compare = Pervasives.compare
1160 module IntSet = Set.Make(IntOT);;
1162 let n_purged = ref 0;;
1164 let collect ((id_to_eq,maxmeta) as bag) alive1 alive2 alive3 =
1166 let p,_,_ = proof_of_id bag id in
1168 | Exact _ -> IntSet.empty
1169 | Step (_,(_,id1,(_,id2),_)) ->
1170 IntSet.add id1 (IntSet.add id2 IntSet.empty)
1173 let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
1174 if IntSet.equal news s then s else close news
1176 let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
1177 let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
1178 let closed_alive_set = close alive_set in
1182 if not (IntSet.mem k closed_alive_set) then
1183 k::s else s) id_to_eq []
1185 n_purged := !n_purged + List.length to_purge;
1186 List.fold_right M.remove to_purge id_to_eq, maxmeta
1189 let get_stats () = ""
1191 <:show<Equality.>> ^
1192 "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"
1196 let rec pp_proofterm name t context =
1197 let rec skip_lambda tys ctx = function
1198 | Cic.Lambda (n,s,t) -> skip_lambda (s::tys) ((Some n)::ctx) t
1203 | Cic.Name s1 -> Cic.Name (s ^ s1)
1206 let rec skip_letin ctx = function
1207 | Cic.LetIn (n,b,_,t) ->
1208 pp_proofterm (Some (rename "Lemma " n)) b ctx::
1209 skip_letin ((Some n)::ctx) t
1211 let ppterm t = CicPp.pp t ctx in
1212 let rec pp inner = function
1213 | Cic.Appl [Cic.Const (uri,[]);_;l;m;r;p1;p2]
1214 when Pcre.pmatch ~pat:"trans_eq" (UriManager.string_of_uri uri)->
1216 (" " ^ ppterm l) :: pp true p1 @
1217 [ " = " ^ ppterm m ] @ pp true p2 @
1218 [ " = " ^ ppterm r ]
1221 [ " = " ^ ppterm m ] @ pp true p2
1222 | Cic.Appl [Cic.Const (uri,[]);_;l;m;p]
1223 when Pcre.pmatch ~pat:"sym_eq" (UriManager.string_of_uri uri)->
1225 | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
1226 when Pcre.pmatch ~pat:"eq_f" (UriManager.string_of_uri uri)->
1228 | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
1229 when Pcre.pmatch ~pat:"eq_OF_eq" (UriManager.string_of_uri uri)->
1231 | Cic.Appl [Cic.MutConstruct (uri,_,_,[]);_;_;t;p]
1232 when Pcre.pmatch ~pat:"ex.ind" (UriManager.string_of_uri uri)->
1233 [ "witness " ^ ppterm t ] @ pp true p
1234 | Cic.Appl (t::_) ->[ " [by " ^ ppterm t ^ "]"]
1235 | t ->[ " [by " ^ ppterm t ^ "]"]
1237 let rec compat = function
1238 | a::b::tl -> (b ^ a) :: compat tl
1242 let compat l = List.hd l :: compat (List.tl l) in
1243 compat (pp false t) @ ["";""]
1245 let names, tys, body = skip_lambda [] context t in
1246 let ppname name = (match name with Some (Cic.Name s) -> s | _ -> "") in
1247 ppname name ^ ":\n" ^
1248 (if context = [] then
1249 let rec pp_l ctx = function
1251 " " ^ ppname name ^ ": " ^ CicPp.pp t ctx ^ "\n" ^
1255 pp_l [] (List.rev (List.combine tys names))
1258 String.concat "\n" (skip_letin names body)
1261 let pp_proofterm t =
1263 pp_proofterm (Some (Cic.Name "Hypothesis")) t []
1266 let initial_nameset_list = [
1267 "x"; "y"; "z"; "t"; "u"; "v"; "a"; "b"; "c"; "d";
1268 "e"; "l"; "m"; "n"; "o"; "p"; "q"; "r";
1271 module S = Set.Make(String)
1273 let initial_nameset = List.fold_right S.add initial_nameset_list S.empty, [];;
1275 let freshname (nameset, subst) term =
1276 let m = CicUtil.metas_of_term term in
1277 let nameset, subst =
1279 (fun (set,rc) (m,_) ->
1280 if List.mem_assoc m rc then set,rc else
1281 let name = S.choose set in
1282 let set = S.remove name set in
1284 (m,Cic.Const(UriManager.uri_of_string
1285 ("cic:/"^name^".con"),[]))::rc)
1289 ProofEngineReduction.replace
1290 ~equality:(fun i t -> match t with Cic.Meta (j,_) -> i=j| _ -> false)
1291 ~what:(List.map fst subst)
1292 ~with_what:(List.map snd subst) ~where:term
1294 (nameset, subst), term
1297 let remove_names_in_context (set,subst) names =
1300 match n with Some (Cic.Name n) -> S.remove n s | _ -> s)
1304 let string_of_id2 (id_to_eq,_) names nameset id =
1305 if id = 0 then "" else
1307 let (_,_,(_,l,r,_),_,_) = open_equality (M.find id id_to_eq) in
1308 let nameset, l = freshname nameset l in
1309 let nameset, r = freshname nameset r in
1310 Printf.sprintf "%s = %s" (CicPp.pp l names) (CicPp.pp r names)
1312 Not_found -> assert false
1315 let draw_proof bag names goal_proof proof id =
1316 let b = Buffer.create 100 in
1317 let fmt = Format.formatter_of_buffer b in
1318 let sint = string_of_int in
1319 let fst3 (x,_,_) = x in
1320 let visited = ref [] in
1321 let nameset = remove_names_in_context initial_nameset names in
1322 let rec fact id = function
1324 if not (List.mem id !visited) then
1326 visited := id :: !visited;
1327 let nameset, t = freshname nameset t in
1328 let t = CicPp.pp t names in
1329 GraphvizPp.Dot.node (sint id)
1330 ~attrs:["label",t^":"^string_of_id2 bag names nameset id;
1331 "shape","rectangle"] fmt;
1333 | Step (_,(_,id1,(_,id2),_)) ->
1334 GraphvizPp.Dot.edge (sint id) (sint id1) fmt;
1335 GraphvizPp.Dot.edge (sint id) (sint id2) fmt;
1336 let p1,_,_ = proof_of_id bag id1 in
1337 let p2,_,_ = proof_of_id bag id2 in
1340 if not (List.mem id !visited); then
1342 visited := id :: !visited;
1343 GraphvizPp.Dot.node (sint id)
1344 ~attrs:["label",sint id^":"^string_of_id2 bag names nameset id;
1345 "shape","ellipse"] fmt
1348 let sleft acc (_,_,id,_,_) =
1349 if acc != 0 then GraphvizPp.Dot.edge (sint acc) (sint id) fmt;
1350 fact id (fst3 (proof_of_id bag id));
1353 GraphvizPp.Dot.header ~node_attrs:["fontsize","10"; ] fmt;
1354 ignore(List.fold_left sleft id goal_proof);
1355 GraphvizPp.Dot.trailer fmt;
1356 let oc = open_out "/tmp/matita_paramod.dot" in
1357 Buffer.output_buffer oc b;
1359 Utils.debug_print (lazy "dot!");
1361 "dot -Tps -o /tmp/matita_paramod.eps /tmp/matita_paramod.dot"
1362 (* "cat /tmp/matita_paramod.dot| tred | dot -Tps -o /tmp/matita_paramod.eps" *)
1364 ignore(Unix.system "gv /tmp/matita_paramod.eps");
1367 let saturate_term (id_to_eq, maxmeta) metasenv subst context term =
1368 let maxmeta = max maxmeta (CicMkImplicit.new_meta metasenv subst) in
1369 let head, metasenv, args, newmeta =
1370 TermUtil.saturate_term maxmeta metasenv context term 0
1372 (id_to_eq, newmeta), head, metasenv, args
1375 let push_maxmeta (id_to_eq, maxmeta) m = id_to_eq, max maxmeta m ;;
1376 let filter_metasenv_gt_maxmeta (_,maxmeta) =
1377 List.filter (fun (j,_,_) -> j >= maxmeta)